Quantum Mechanics and Spectrum Generating Groups and Supergroups


In our quantum mechanics course we were taught that molecules consist of N electrons and M nuclei and that one has to solve a (N + M) body Schrödinger equation to understand their structure. But if one looks at the work of the practitioners in this area, e.g. the books of G. Herzberg,1) one sees that the practice is different: Low energy spectra and structure of molecules are analyzed in terms of rotators and oscillators (and at slightly higher energies in terms of Kepler systems (one electron outside a core)). This is shown in Figure la.


Rotational Band Vibrational Excitation Collective Model Supersymmetric Quantum Mechanic Group Contraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and Footnotes

  1. 1).
    G. Herzberg, Molecular Spectra and Molecular Structure, D. van Norstrand Publishers (1966).Google Scholar
  2. 2).
    A. O. Barut, A. Bohm, Phys. Rev. 139B, 1107 (1965)CrossRefGoogle Scholar
  3. Y. Dothan, M. Gell-Mann, Y. Ne’eman, Phys. Lett. 17, 145 (1965)CrossRefGoogle Scholar
  4. N. Mukunda, L. O’Raifeartaigh, E.C.G. Sudarshan, Phys. Lett 15, 1041 (1965)CrossRefGoogle Scholar
  5. I. A. Malkin V. Manko JETP, Letters 2, 230 (1965).Google Scholar
  6. No attempt will be made to distinguish between the terms dynamical group, spectrum generating groups, spectrum algebras, spectrum supersymmetry, etc.Google Scholar
  7. 3).
    A. Bohr, B. Mottelson, Nuclear Structure Vol. II, Benjamin (1969).Google Scholar
  8. 4).
    A. Arima, F. Iachello, Phys. Rev. Lett. 35, 1065 (1975)CrossRefGoogle Scholar
  9. F. Tachello, in Supersymmetry in Physics, p. 85, V. A. Kostelecky, David K. Campbell, editors, North-Holland, 1985.Google Scholar
  10. 5).
    S. Goshen, H. J. Lipkin, Ann. of Phys. 6, 301 (1959).CrossRefGoogle Scholar
  11. 6).
    G. Rosensteel, D. J. Rowe, in Group Theoretical Methods in Physics, p. 115, R. T. Sharp, et al., editors, Academic Press, 1977.Google Scholar
  12. 7).
    This latter dualism is only part of a more general pluralism“ (E. P. Wigner).Google Scholar
  13. 8).
    A. Bohm, M. Loewe, P. Magnollay, Phys. Rev. D32, 791 (1985)Google Scholar
  14. A. Bohm, M. Loewe, P. Magnollay, Phys. Rev. Lett. 53, 2292 (1984).CrossRefGoogle Scholar
  15. A Bohm, M. Loewe, P. Magnollay, L. C. Biedenharn, H. van Dam, M. Tarlini, R. R. Aldinger, Phys. Rev. D32, 2828 (1985).Google Scholar
  16. 9).
    P. A. M. Dirac, Lectures on Quantum Mechanics, Yeshiva University Press (1984)Google Scholar
  17. N. Mukunda, H. van Dam, L. C. Biedenharn, Relativistic Models, Springer Verlag, N.Y. (1982), Chapter V.Google Scholar
  18. 10).
    E.g. J. Scherk, Rev. Mod. Phys. 47, 123 (1975).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • A. Bohm
    • 1
  1. 1.Center for Particle Theory, Deparment of PhysicsThe University of Texas at AustinAustinUSA

Personalised recommendations